1. School of Mechanical Engineering FACULTY OF ENGINEERING School of Mechanical Engineering FACULTY OF ENGINEERING Thin Film Coating and Small Scale Fluid Dynamics Rob Hewson Nik Kapur Jon Summers Harvey Thompson

2. School of something FACULTY OF OTHER School of Mechanical Engineering FACULTY OF ENGINEERING

3. School of something FACULTY OF OTHER School of Mechanical Engineering FACULTY OF ENGINEERING Engineers / physicists / mathematicians within group who are well equipped to model & experiment on flows & specify designs (both continuum and non-continuum) Wide range of applications including Fluid coating Lubrication Printing Droplet coalescence and dynamics

4. School of something FACULTY OF OTHER School of Mechanical Engineering FACULTY OF ENGINEERING Thin Film Fluid Coatings LEVELTHIN FAST versus Method must be: Flexible Reliable

5. School of something FACULTY OF OTHER School of Mechanical Engineering FACULTY OF ENGINEERING Thin Film Fluid Coatings Curtain Coating Gravure Roll Coating Roll Coating Slot Coating Dip Coating Slide Coating

6. School of something FACULTY OF OTHER School of Mechanical Engineering FACULTY OF ENGINEERING U2U2 WEB SPEED FLUID DOCTOR BLADE CELL GEOMETRY Discrete Trihelical Thin Film Fluid Coatings Gravure Roll Coating Multi-scale Multiphase Flexible boundaries Pickout at upstream meniscus Cells affect pressure gradient within bead Cells enter full Cells leave fractionally full

7. School of something FACULTY OF OTHER School of Mechanical Engineering FACULTY OF ENGINEERING As speed ratio increases pickout increases film thickness also increase to a maximum then reduces Reasonable agreement with experimental 3D discrete cell results of Kapur (2003) Thin Film Fluid Coatings Gravure Roll Coating results

8. School of something FACULTY OF OTHER School of Mechanical Engineering FACULTY OF ENGINEERING Coated Substrate Wiper Reservoir Industrially- important variation of the robust reverse roll configuration used for manufacturing a variety of films and foils Reservoir-fed Reverse Roll Coating

9. School of something FACULTY OF OTHER School of Mechanical Engineering FACULTY OF ENGINEERING Reservoir-fed Reverse Roll Coating Finite Element Meshes

10. School of something FACULTY OF OTHER School of Mechanical Engineering FACULTY OF ENGINEERING Reservoir-fed Reverse Roll Coating: Comparison with Experiment

11. Finite Element methods not as well-established for 3-D free surface flow. Promising alternatives include Level- Set, Volume of Fluid (VoF), Lattice Boltzmann etc… x y  h(x,y) s(x,y) gravity inflow outflow z L0L0 H0H0 School of Mechanical Engineering FACULTY OF ENGINEERING

12. 2-D Flow of Water Film over a Trench Topography (e=0) Comparison between experimental free surface profiles and those predicted by solution of the full Navier-Stokes and Lubrication equations. Agreement is very good between all data. Lubrication theory is accurate. School of Mechanical Engineering FACULTY OF ENGINEERING

13. School of Mechanical Engineering FACULTY OF ENGINEERING

14. Flow over a Trench topography H 0 =100  m, s 0 =0.5,  0 =0.001, c 0 =0.7: Solvent Concentration is affected by topography School of Mechanical Engineering FACULTY OF ENGINEERING

15. Flow past a square trench: sides 0.1x0.1 (no evaporation) Evolution of time-dependent solutions to to steady-state Grid adaptivity follows the flow development t=0.1 t=0.2 t=0.3 t=1.0 (steady) School of Mechanical Engineering FACULTY OF ENGINEERING

16. Flow past a square trench topography: base uniform grid is 33x33 (a)Grid adaptivity near (green) (b) CPU saving from limiting trench for base 33x33 grid refinement from 33x33 base grid according to RTE Savings particularly important for small topographies where fine base grids are needed! School of Mechanical Engineering FACULTY OF ENGINEERING

17. Flow Over Flexible Substrates Free surface disturbances on flexible substrates are suppressed. Useful in manufacturing processes such as photolithography Flow over Single Trench Flow over Complex Circuit School of Mechanical Engineering FACULTY OF ENGINEERING

18. School of Mechanical Engineering FACULTY OF ENGINEERING

19. Curtain coating experiments by Kodak indicate that the dynamic contact angle depends not only on web speed, but on flow rate as well. School of Mechanical Engineering FACULTY OF ENGINEERING

20. air entrainment OK Experiments by H. Benkreira – Chem. Eng. Sci. 2004 Experiments by Kodak rougher smoother microscale influence 10 -8 … 10 -7 m macroscale influence 10 -3 … 10 -2 m Simultaneous, competing influences Work of Lydéric Bocquet, et al. School of Mechanical Engineering FACULTY OF ENGINEERING

21. School of something FACULTY OF OTHER School of Mechanical Engineering FACULTY OF ENGINEERING Modelling Small Scale Fluid Processes Conventional fluid dynamics well suited to many engineering situations (FE analysis) Boundary conditions control flow – many assumed Must handle surface effects Chemistry Slip Phase change Geometry at nano- & micro- scale Alternate methods: Lattice Boltzmann systems Molecular dynamic systems …

22. Contact Angle Versus Speed Experiments of Blake et al. J. Colloid Interf. Sci. 253,196 (2002) Ca Lattice Boltzmann results School of Mechanical Engineering FACULTY OF ENGINEERING

23. Wetting Failure u=0.0027 entrainment! u=0.0024 stable u=0.0021 stable u=0.0018 stable u=0.0015 stable light phase dense phase body force (gravity) School of Mechanical Engineering FACULTY OF ENGINEERING

24. Surface Tension Relaxation Solid-Liquid Interface u increasing School of Mechanical Engineering FACULTY OF ENGINEERING

25. Heterogeneous Surfaces u>0 u<0 u=0 uniform wettability sinusoidally varying wettability contact angle hysteresis School of Mechanical Engineering FACULTY OF ENGINEERING

26. School of something FACULTY OF OTHER School of Mechanical Engineering FACULTY OF ENGINEERING Lattice Boltzmann Simulations Body force drives fluid  S =20°  S =90°  S =160°

27. School of something FACULTY OF OTHER School of Mechanical Engineering FACULTY OF ENGINEERING Non-uniform wettability – patches of different contact angle

28. Combined numerical and experimental effort. School of Mechanical Engineering FACULTY OF ENGINEERING

29. Coating Area of low contact angle Area of high contact angle Initial droplet profile School of Mechanical Engineering FACULTY OF ENGINEERING

30. Coating School of Mechanical Engineering FACULTY OF ENGINEERING

31. It is well known that droplet spreading with evaporation can lead to the Coffee-Stain effect – ring of solid formed after solvent has evaporated. As solvent depleted from edge, viscosity rises sharply and pins the drop. As surface tension at edges is larger than in centre, fluid is pulled towards the edge, thus forming the coffee-stain. Evolution of Drop Cross-Section Marangoni Effect needed to produce the stain! School of Mechanical Engineering FACULTY OF ENGINEERING

32. We now consider droplet migration up an inclined plane under the action of surface energy gradient and topographic barriers. Chaudhury & Whitesides (1992) studied water droplets on an inclined silicon wafer treated with dicyltrichlorosilane to create required surface energy gradient. Initial drop radius = 1mm up a slope with angle α=15 o with no topography, initial θ e = 30 o Again, h * has important effect on spreading rate. Good agreement with experimental speed (1.4mm/s) for h * ≤ 3µm. α School of Mechanical Engineering FACULTY OF ENGINEERING

33. School of something FACULTY OF OTHER School of Mechanical Engineering FACULTY OF ENGINEERING Droplet Dynamics Droplet coalescence is an important phenomenon in practical applications such as ink-jet printing, microfluidic devices,…, Coalescence of two droplets on a solid surfaces using simple experimental apparatus:

34. School of Mechanical Engineering FACULTY OF ENGINEERING

35. Lubrication modelling Uses simplification of Navier-Stokes equations for systems where typical heights << typical lengths Assumes slopes are small contact angles should be small, but… Assumes presence of a precursor film, thickness 1-100nm? Contact angles included via a disjoining pressure School of Mechanical Engineering FACULTY OF ENGINEERING

36. Lattice Boltzmann Modelling Lattice Botzmann Method Use ‘finite-density’ multiphase approach He et al. (1997…) Based on Enskog equation Two distribution functions D3Q19 lattice Single-relaxation time, BGK Bounce-back & periodic boundary conditions Surface affinity of Iwahara et al. (2003) School of Mechanical Engineering FACULTY OF ENGINEERING

37. LBM vs Physical Scales Two key length scales in the problem Interface thickness Drop size Matching interface thickness severely restricts problem size 20 billion nodes for 1mm drop if h=10 -8 m Matching drop size grossly exaggerates equivalent interface thickness School of Mechanical Engineering FACULTY OF ENGINEERING

38. Results: Top View Lubrication theoryExperimentsLattice Boltzmann θ eq = 45° School of Mechanical Engineering FACULTY OF ENGINEERING

39. Results: Top View Lubrication theoryExperimentsLattice Boltzmann θ eq = 45° School of Mechanical Engineering FACULTY OF ENGINEERING

40. Side View ExperimentsLattice Boltzmann School of Mechanical Engineering FACULTY OF ENGINEERING

41. Neck Height - Experiments Note oscillations No oscillations Final height too low Time scales do not match Get first overshoot School of Mechanical Engineering FACULTY OF ENGINEERING

42. Effect of Surface Patterning Specification of surface affinity (α s ) can be a function of space Non-homogeneous wettability Contact angle hysteresis Localized pinning Effective in 2D filament studies (last year) Set up a chequerboard pattern of two different values of α s How does it change droplet footprint? School of Mechanical Engineering FACULTY OF ENGINEERING

43. Effect of Surface Patterning uniform 2x2 4x4 10x10 θ eq = 45° ± 2° School of Mechanical Engineering FACULTY OF ENGINEERING